Have Cat Questions? Ask a Cat Vet Online.
Your cat could have allergies, mange, dry skin....
Cats don't just have allergies to food. They also have allergies to products, household cleaning solutions and fleas. It only takes one flea to start the process and it might continue even after the fleas are gone. A skin scraping will rule out demodectic and sarcoptic mange. Sarcoptic mange is contagious and demodectic is not. Demodectic is caused more by a compormised immune system. He can also provide meds that will help with hair loss, any secondary fungal infections and will make your cat feel better.
Some cats get a great deal of relief from a diet change to a low allergy diet. Your vet can help you pick a product that will be best for your cat.
If you don't have the cat on frontline or other prescription flea product, you will want to do that as soon as you can.
You should also get the cat started on a supplement that contains omega three fatty acids. Good skin starts on the inside.
The hair loss under the chin could be feline acne. If you suspect this, you will want to discontinue use of metal bowls and be sure to sanitize them well. You can also try an over the counter acne medication and see if it helps.Good luck!
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FYI - you can also have a vet visit your home to treat the cat.